"I felt that maybe she wasn't feeling well", she said.
The Romanian finally put away the 114th ranked Kozlova with eight consecutive points in the second set, a backhand victor proving the decider just as it had in the first set.
Tennis superstar Serena Williams was forced off court during her BNP Paribas Open match at Indian Wells against Garbine Muguruza on Sunday after experiencing "extreme fatigue" brought on by a viral infection.
Williams had taken a 3-0 lead in the first set before losing the next seven games.
"We've played many times and it is always super tough and super exciting".
Following up on a strong showing Friday against Victoria Azarenka, the 23-time Grand Slam victor took a 3-0 lead over Muguruza, but lost the next six games and the first set.
"By the score, it might have looked like I started well, but I was not feeling at all well physically", Williams said.
However, Williams - who entered the tournament as the 10th seed - was not moving freely and Muguruza battled back with a series of stunning groundstrokes of her own. "I will focus on getting better and start preparing for Miami".
Serena Williams bowed out of the Indian Wells Open due to illness, while Simona Halep and Elina Svitolina enjoyed strong wins. As long as Venus has her return working and is spraying winners, you can live with an inconsistent serve and a higher number of break points. The next was the 2016 French final, where Murguruza won 7-5, 6-4.
World No.97 Barthel, a former Top 25 player, notched her second Top 20 win in a row with a third-round upset of her countrywoman Julia Goerges, the No.15 seed, 7-5, 1-6, 6-4.
Halep, the 2015 champion, was challenged but got past qualifier Kateryna Kozlova 7-6 (7-3) 7-5.